MACHINE DRAWING & COMPUTER GRAPHICS
X= xh
,
153
y= yh
h
h
A general homogeneous coordinate representation can also be written as (h.x,h.y,h).
The term homogeneous coordinates is used in mathematics to refer to the effect of this representation on Cartesian equations.
When a Cartesian point (x,y)is converted to a homogeneous representation (xh,yh,h),equations containing x and y , such as f(x,y)=0, become homogeneous equations in the three parameters xh,yh, and h. This just means that if each of the three parameters is replaced by any value v times that parameter; the value v can be factored out of the equations. For translation we have
P’= T(tx,ty).P
Rotation transformation equations about the coordinate origin are written as
P’=R(θ).P
A scaling transformation relative to the coordinate origin is
P’=S(sx,sy).P
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